Find the ratio of LCM to HCF of the numbers 99 and 15.

Two numbers: 99 and 15

The ratio of the LCM (Least Common Multiple) to the HCF (Highest Common Factor) of two numbers is calculated as:

​$$\text{Ratio} = \frac{\text{LCM of the numbers}}{\text{HCF of the numbers}}$$​​

Prime Factorization:

99 = $$3^2 \times 11$$​​

15 = $$3 \times 5$$​​

For HCF:

The common factor between 99 and 15 is 3.

Hence, HCF = 3.

For LCM:

LCM = $$3^2 \times 5 \times 11 = 9 \times 5 \times 11$$​ = 495

Now,

​$$\text{Ratio} = \frac{\text{LCM}}{\text{HCF}} = \frac{495}{3} = \frac{165}{1}$$​​

Thus, the ratio of LCM to HCF is 165 : 1.